Cannon, the son of Emma McAfee and William Ragsdale Cannon, was born on April 5, 1916, in Chattanooga, Tennessee. Raised in Dalton, Georgia, he graduated from the University of Georgia in Athens in 1937 and from Yale Divinity School in New Haven, Connecticut, in 1940. He received a Ph.D. from Yale University in 1942. He never married.

Cannon served churches in Oxford before joining Candler's faculty in 1943. Beginning in 1948 he was regularly elected to jurisdictional and general conferences until he was chosen bishop in 1968. During his tenure as bishop, Cannon served as the episcopal (meaning of or related to bishops) leader of the Raleigh Area (1968-72 and 1980-84) in North Carolina, the Richmond Area (1970-72) in Virginia, and the Atlanta Area (1972-80).

As dean of Candler in the mid-1960s, Cannon defended Emory's retention of religion professor Thomas J. J. Altizer, a proponent of the death-of-God position. This position later came to be known as the "God is dead" controversy. Cannon also guided Candler through racial integration.

influential in the Council of Bishops, Cannon delivered the 1984 Episcopal Address—the highest honor conferred on a council member. As a bishop he stressed Christian education and evangelism, and was known for his classically orthodox, Wesleyan positions.

During his career Cannon participated in Methodist conversations with Lutheran, Reformed, and Roman Catholic leaders and scholars. A Protestant observer at Vatican Council II in 1965 and the Extraordinary Synod of the Roman Catholic Church in 1985, he became friends with Pope John Paul II, who sent a statement to be read at Cannon's funeral.

Cannon retired to Georgia in 1984, becoming bishop-in-residence at Northside United Methodist Church in Atlanta. In 1994 he was a principal founder of the Confessing Movement, which focused on the United Methodist Church's mission to"retrieve its classical doctrinal identity, and to live it out as disciples of Christ." Cannon died in Crawford Long Hospital in Atlanta in 1997 and is buried in West Hill Cemetery in Dalton. Cannon Chapel at Emory is named in his honor.